You can use the Mathway widget below to
practice solving a radical equation. Try the entered exercise, or
type in your own exercise. Then click "Answer" to compare your
answer to Mathway's. (Or skip the widget and continue
with the lesson.)

(Clicking on "View Steps"
on the widget's answer screen will take you to the Mathway site, where
you can register for a free seven-day trial of the software.)

This already has the
square root by itself on one side, so I can proceed directly to squaring
both sides. However, a great many students will do the following when
given this type of question:

<== (wrong!)

Do you see how the student
erroneously "distributed" the square through the parentheses?
Do you see how the student squared terms,
not sides? In so doing, the student has arrived at a result which, technically
speaking, means that every single value of x
will work, since it appears that the equation is always true everywhere.
(When would zero not be equal to zero, right?) But the graph
of the equations of the two sides:

ADVERTISEMENT

...shows otherwise:

And, from your experience
graphing straight
lines and radical
functions, you
should already have known that there was no way that a curvy radical
line could possibly be the same as a straight line such asy
= 3x + 2.

So don't square terms;
square sides! And take the time to write out the square properly: